Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
182 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16811657 | C2 | semidirect |
| 2. #16811651 | C2 | semidirect |
| 3. #16811487 | C2 | semidirect |
| 4. #16811471 | C2 | semidirect |
| 5. #16811471 | C2 | semidirect |
| 6. #88324⋊C8 | C2 | semidirect |
| 52. D212 | M16 | semidirect |
| 61. #88324 | D8 | semidirect |
| 91. C53 | #1581 | semidirect |